Cooperation in spatial prisoner's dilemma game with delayed decisions

Phenomena that time delays of information lead to delayed decisions are extensive in reality. The effect of delayed decisions on the evolution of cooperation in the spatial prisoner's dilemma game is explored in this work. Players with memory are located on a two dimensional square lattice, and they can keep the payoff information of his neighbors and his own in every historic generation in memory. Every player uses the payoff information in some generation from his memory and the strategy information in current generation to determine which strategy to choose in next generation. The time interval between two generations is set by the parameter m. For the payoff information is used to determine the role model for the focal player when changing strategies, the focal player's decision to learn from which neighbor is delayed by m generations. Simulations show that cooperation can be enhanced with the increase of m. In addition, just like the original evolutionary game model (m = 0), pretty dynamic fractal patterns featuring symmetry can be obtained when m > 0 if we simulate the invasion of a single defector in world of cooperators on square lattice.